1. Field of the invention
The present invention relates to permanent magnet (PM) synchronous machines and, more particularly, to a quasi square-wave brushless DC machine incorporating five or more phases for increased efficiency and/or torque density.
2. Description of the Background
Consider a pole pair of a generic permanent magnet synchronous linear machine as shown in FIG. 1. The direction of rotor movement is along the x-axis, and this is perpendicular to the y-directed magnetic flux flow across air gap 2. The current I through the phase windings of the stator can be represented by an equivalent z-directed sheet current K.sub.sz (x) at point 4 because the sheet current K.sub.sz (x) produces the same fields as those which would otherwise be produced by actual stator windings. At the position 4 of the equivalent sheet current K.sub.sz (x), the tangential (or x-directed) component of surface force density (or stress) f.sub.z is given by: EQU f.sub.z (x)=-K.sub.sz (x)B.sub.my (x) (N/m.sup.2)
where B.sub.my (x) is the normal or y-directed component of magnetic flux density through the air gap 2 due to the rotor magnet 6.
The net instantaneous force per pole F.sub.p per unit active width of the machine of FIG. 1 is then given by: ##EQU1## where the distance x.sub.p is a pole pitch.
It is obvious from equation (1) that for maximum motoring (or generating) force per ampere of stator current we must have the stator sheet current K.sub.sz (x) and air gap 2 magnetic flux density B.sub.my (x) spatially and temporally in phase (anti-phase for generation).
FIG. 2 gives a simple example for a sinusoidally varying stator sheet current K.sub.sz (x) which is in-phase with a sinusoidally varying magnetic flux density B.sub.my (x) at air gap 2. For peak flux density B.sub.m and peak sheet current density K.sub.s, equation (1) can be solved as follows for the net force per pole F.sub.p for the perfectly in-phase drive of FIG. 2: EQU F.sub.p =-K.sub.s B.sub.m x.sub.p /2.
It is known that single frequency sinusoidal line voltage and current machines do not fully utilize the available "active" regions at the air gap 2. More specifically, the driving stress at the stator surface peaks at the pole centers when the rotor magnets reach alignment with a stator current sheet, but towards the mid-pole regions of air gap 2, the drive stress falls to zero. Hence, the net force per pole F.sub.p for a perfectly in-phase AC sinusoidal drive is unduly low in comparison to "square-wave" machines.
Permanent magnet synchronous machines which operate from square-wave input signals make better use of the air gap 2 periphery.
FIG. 3 gives an example for a three-phase machine operating from a quasi-square wave (a.k.a. trapezoidal) stator sheet current K.sub.sz (x) which is in-phase with a square-wave magnetic flux density B.sub.my (x) at air gap 2. For square-wave machines, let the fraction m.sub.p equal that portion of a full pole pitch which, at any one time, has full stator sheet current excitation at maximum value K.sub.s.quadrature.. For the same RMS heating as in the above-described sinusoidal drive and for equal amounts and even distribution of stator copper, the maximum square-wave stator excitation current must relate to the maximum sinusoidal stator excitation current as follows: ##EQU2##
Again solving equation (1) for a square-wave machine with square waves of magnetic flux and current drive, and for peak flux density B.sub.m and peak sheet current density K.sub.s.quadrature., the net force per pole F.sub.p for a perfectly in-phase drive is -K.sub.s.quadrature. B.sub.m m.sub.p x.sub.p. Thus, with equal I.sup.2 r heating losses, the quasi-square wave machine generates a force per pole F.sub.p which exceeds that of an otherwise equivalent sinusoidal AC machine by an improvement factor of .sqroot.2m.sub.p . Since three-phase quasi square-wave (trapezoidal) back emf machines have approximately constant current flow in two of the three stator phase windings at any one time, the fraction of rotor magnet use m.sub.p equals 2/3, and the above-described improvement factor under ideal conditions equals .sqroot.4/3, or 1.16.
The improvement factor can be elevated even further by constructing a quasi square-wave back emf PM machine with a greater number of phases. For instance, a five phase machine would have 4/5 of the rotor magnets active, and the improvement factor would equal .sqroot.8/5 or 1.27. It should be noted that the incremental gain in the improvement factor falls off rapidly for phase orders exceeding five phases. For example, the improvement factors for 7, 9, and 11 phase machines are 1.31, 1.33, and 1.35, respectively.
Higher phase order square wave PM machines also make better use of the solid-state switching devices in their switched drive systems (relative to their three-phase counter parts). Specifically, if the machine peak stator phase winding current has value Im, and the peak machine line-to-line back emf has value E.sub.m, then the required peak volt-amp performance for an n-phase machine is (n-1)E.sub.m I.sub.m /2. Moreover, an n-phase machine requires 2n switching devices in the accompanying solid state inverter drive system, and each switch must be capable of blocking at least E.sub.m volts and conducting at least I.sub.m amps. The total volt-amp rating of the inverter is thus 2nE.sub.m I.sub.m. The ratio of inverter volt-amps to machine volt-amps is then 4n/(n-1), which for 3, 5, 7, and 9 phase machines has values of 6, 5, 4.67, and 4.5, respectively. Again, we see better results as the phase order increases, and the largest incremental advantage occurs in the 5-phase machine.
Consequently, it would be greatly advantageous to provide a higher phase-order (five or more) quasi square-wave back emf permanent magnet machine which capitalizes on the above-described efficiencies.